The most common and most likely answer to this crossword clue is the 7 plus 6 letter word LUNATIC FRINGE
I've seen this crossword clue in The Times
L
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N
A
T
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F
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More clues leading to the result LUNATIC FRINGE
- Finger broken after headcase forms group of extremists
- I felt uncaring somehow in group of political extremists
- Finger given by this less restrained element?
- Political fanatics unfit, clearing off
- Eccentric minority’s bizarre fencing ritual
- Political extremists enact ruling if wrong
- Maybe finger the idiotic extremists
- Ridiculous hairstyle worn by very extreme people?
- Extreme left or extreme right in centrifugal force
Buddy explains!

The straight part
We know that "group of political extremists" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case group of political extremists = lunatic fringe.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.